Merge branch 'master' of https://github.com/yashrajgupta/IntervalArithmetic.jl into rsqrt_function_patch

Author: yashrajgupta

src/IntervalArithmetic.jl

@@ -29,7 +29,7 @@ import Base:
     convert, promote_rule, eltype, size,
     BigFloat, float, widen, big,
     ∩, ∪, ⊆, ⊇, ∈, eps,
-    floor, ceil, trunc, sign, round,
+    floor, ceil, trunc, sign, round, copysign, flipsign, signbit,
     expm1, log1p,
     precision,
     isfinite, isnan, isinf, iszero,

src/intervals/arithmetic.jl

@@ -354,6 +354,43 @@ function sign(a::Interval)
     return Interval(sign(a.lo), sign(a.hi))
 end
 
+"""
+    signbit(x::Interval)
+
+Returns an interval containing `true` (`1`) if the value of the sign of any element in `x` is negative, containing `false` (`0`)
+if any element in `x` is non-negative, and an empy interval if `x` is empty.
+
+# Examples
+```jldoctest
+julia> signbit(@interval(-4))
+[1, 1]
+
+julia> signbit(@interval(5))
+[0, 0]
+
+julia> signbit(@interval(-4,5))
+[0, 1]
+```
+"""
+function signbit(a::Interval) 
+    isempty(a) && return emptyinterval(a)
+    return Interval(signbit(a.hi), signbit(a.lo))
+end
+
+for Typ in (:Interval, :Real, :Float64, :Float32, :Signed, :Unsigned)
+    @eval begin
+        copysign(a::$Typ, b::Interval) = abs(a)*(1-2signbit(b))
+        flipsign(a::$Typ, b::Interval) = a*(1-2signbit(b))
+    end
+end
+
+for Typ in (:Real, :Float64, :Float32, :Signed, :Unsigned)
+    @eval begin
+        copysign(a::Interval, b::$Typ) = abs(a)*(1-2signbit(b))
+        flipsign(a::Interval, b::$Typ) = a*(1-2signbit(b))
+    end
+end
+
 # RoundTiesToEven is an alias of `RoundNearest`
 const RoundTiesToEven = RoundNearest
 # RoundTiesToAway is an alias of `RoundNearestTiesAway`

test/interval_tests/numeric.jl

@@ -192,6 +192,39 @@ end
     @test ceil(@interval(0.1, 1.1)) == Interval(1, 2)
     @test round(@interval(0.1, 1.1), RoundUp) == Interval(1, 2)
     @test sign(@interval(0.1, 1.1)) == Interval(1.0)
+    @test signbit(@interval(-4)) == @interval(1,1)
+    @test signbit(@interval(5)) == @interval(0,0)
+    @test signbit(@interval(-4,5)) == @interval(0,1)
+    @test copysign(@interval(1,2), @interval(-1,1)) == @interval(-2,2)
+    @test copysign(3, @interval(-1,1)) == @interval(-3,3)
+    @test copysign(3.0, @interval(-1,1)) == @interval(-3,3)
+    @test copysign(3f0, @interval(-1,1)) == @interval(-3,3)
+    @test copysign(3, @interval(0,1)) == @interval(3) == @interval(copysign(3,0),copysign(3,1))
+    @test copysign(3, @interval(-1,0)) == @interval(-3,3) == @interval(copysign(3,-1),copysign(3,0))
+    @test copysign(UInt64(3), @interval(-1,1)) == @interval(-3,3)
+    @test copysign(BigFloat(3), @interval(-1,1)) == @interval(-3,3)
+    @test copysign(@interval(0,1), -1) == @interval(-1,0)
+    @test copysign(@interval(0,1), -1.0) == @interval(-1,0)
+    @test copysign(@interval(0,1), -1f0) == @interval(-1,0)
+    @test copysign(@interval(0,1), -BigFloat(1)) == @interval(-1,0)
+    @test copysign(@interval(0,1), UInt64(1)) == @interval(0,1)
+    @test copysign(@interval(-1),@interval(-1)) == @interval(-1)
+    @test copysign(@interval(-2,2), 2) == @interval(0,2)
+    @test flipsign(@interval(1,2), @interval(-1,1)) == @interval(-2,2)
+    @test flipsign(@interval(1,2), @interval(1,2)) == @interval(1,2)
+    @test flipsign(3, @interval(-1,1)) == @interval(-3,3)
+    @test flipsign(3.0, @interval(-1,1)) == @interval(-3,3)
+    @test flipsign(3f0, @interval(-1,1)) == @interval(-3,3)
+    @test flipsign(3, @interval(0,1)) == @interval(3,3) == @interval(flipsign(3,0),flipsign(3,1))
+    @test flipsign(3, @interval(-1,0)) == @interval(-3,3) == @interval(flipsign(3,-1),flipsign(3,0))
+    @test flipsign(UInt64(3), @interval(-1,1)) == @interval(-3,3)
+    @test flipsign(BigFloat(3), @interval(-1,1)) == @interval(-3,3)
+    @test flipsign(@interval(0,1), -1) == @interval(-1,0)
+    @test flipsign(@interval(0,1), -1.0) == @interval(-1,0)
+    @test flipsign(@interval(0,1), -1f0) == @interval(-1,0)
+    @test flipsign(@interval(0,1), -BigFloat(1)) == @interval(-1,0)
+    @test flipsign(@interval(0,1), UInt64(1)) == @interval(0,1)
+    @test flipsign(@interval(-1),@interval(-1)) == @interval(1)
     @test trunc(@interval(0.1, 1.1)) == Interval(0.0, 1.0)
     @test round(@interval(0.1, 1.1), RoundToZero) == Interval(0.0, 1.0)
     @test round(@interval(0.1, 1.1)) == Interval(0.0, 1.0)